TL;DR: Joseph Fort Newton.
Looks like Joseph Fort Newton. I've looked through the discussion on Wikiquote, which is the basis for my research here.
Dominique Pire, upon receiving the Nobel Prize, sourced it to 'Newton'. Just Newton. After that, it appears to be attributed to Isaac Newton, who is what most people think of when they hear 'Newton' (actually, more people might think of Fig Newtons, but not in the context of people (but who knows, people are weird)).
This site (in French, used Google Translate) claims that's it's Joseph Fort, but don't provide a source.
This however is itself a paraphrasing of the actual writing, to wit. JF's 1948 book "Adventures of Faith" pp 51-52 (((Why are so many people shy, lonely, shut up within themselves, unequal to their tasks, unable to be happy? Because they are inhabited by fear, like the man in the Parable of the Talents, erecting walls around themselves instead of building bridges into the lives of others; shutting out life.")))
And indeed, this appears to be the case.
Here's the book on Amazon.
I then searched for it on Google Books, and found a copy with snippet view and performed a search for 'walls'.
And I found it on page 52:
But it's actually a misquote. It's a paraphrase of the original quote that became popular and mis-attributed.